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Instructions: Please write a thorough, well-organized essay to answer each question. Three civilizations developed from the Roman Empire. Identity and compare these three new civilization in the Early Middle Ages


Definitions:

Risk-Free Rate

The theoretical return on investment with no risk of financial loss, typically represented by the yield on government securities.

Standard Deviation

A statistical measure that quantifies the amount of variability or dispersion around an average.

Optimal

The most favorable or desirable condition, outcome, or level, often in terms of efficiency or success.

Minimum-Variance Portfolio

A portfolio constructed to achieve the lowest possible risk (variance) for a given rate of expected return, optimizing risk-adjusted returns.

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